Răspuns:
[tex]x\cdot y = \frac{1}{101} \\ [/tex]
Explicație pas cu pas:
[tex]x = \frac{1}{2} \cdot \frac{3}{4} \cdot \frac{5}{6} \cdot \frac{7}{8} \cdot...\cdot \frac{99}{100} \\ [/tex]
[tex] y = \frac{2}{3} \cdot \frac{4}{5} \cdot \frac{6}{7} \cdot \frac{8}{9} \cdot...\cdot \frac{100}{101} \\ [/tex]
[tex]x\cdot y = \frac{1}{ \not2} \cdot \frac{ \not2}{ \not3} \cdot \frac{ \not 3}{ \not4} \cdot \frac{ \not4}{ \not5} \cdot \frac{ \not5}{ \not6} \cdot \frac{ \not6}{ \not7} \cdot \frac{ \not7}{ \not8} \cdot \frac{ \not8}{ \not9} \cdot...\cdot \frac{ \not99}{ \not100} \cdot \frac{ \not100}{101} = \boxed{ \frac{1}{101} } \\ [/tex]
